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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

   

 

The $ C^*$-algebra of the exponential function


Author: Klaus Thomsen
Journal: Proc. Amer. Math. Soc. 142 (2014), 181-189
MSC (2010): Primary 46L35, 46L80
Published electronically: September 12, 2013
MathSciNet review: 3119193
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Abstract: The complex exponential function $ e^z$ is a local homeomorphism and therefore gives rise to an étale groupoid and a $ C^*$-algebra. We show that this $ C^*$-algebra is simple, purely infinite, stable and classifiable by K-theory, and has both K-theory groups isomorphic to $ \mathbb{Z}$. The same methods show that the $ C^*$-algebra of the anti-holomorphic function $ \overline {e^z}$ is the stabilisation of the Cuntz-algebra $ \mathcal O_3$.


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Additional Information

Klaus Thomsen
Affiliation: Institut for matematiske fag, Ny Munkegade, 8000 Aarhus C, Denmark
Email: matkt@imf.au.dk

DOI: http://dx.doi.org/10.1090/S0002-9939-2013-11716-8
Received by editor(s): September 23, 2011
Received by editor(s) in revised form: February 24, 2012
Published electronically: September 12, 2013
Communicated by: Marius Junge
Article copyright: © Copyright 2013 American Mathematical Society